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Divisibility Rules Worksheet

Vedic maths trick 13: Divisibility tests · Set 161 · 40 sums
TalentJR

The trick (Ekadhikena Purvena): 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3). Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

NameDateTime takenScore ___ / 40
  1. 1.Is 22366 divisible by 12?
  2. 2.Is 98519 divisible by 23?
  3. 3.Is 188880 divisible by 30?
  4. 4.Is 34568 divisible by 29?
  5. 5.Is 97071 divisible by 19?
  6. 6.Is 51799 divisible by 17?
  7. 7.Is 8337 divisible by 2?
  8. 8.Is 24931 divisible by 13?
  9. 9.Is 56641 divisible by 30?
  10. 10.Is 5368 divisible by 3?
  11. 11.Is 2420 divisible by 11?
  12. 12.Is 92376 divisible by 18?
  13. 13.Is 40506 divisible by 17?
  14. 14.Is 15315 divisible by 3?
  15. 15.Is 36780 divisible by 12?
  16. 16.Is 14950 divisible by 10?
  17. 17.Is 83172 divisible by 12?
  18. 18.Is 60115 divisible by 20?
  19. 19.Is 96480 divisible by 15?
  20. 20.Is 11867 divisible by 12?
  21. 21.Is 77600 divisible by 20?
  22. 22.Is 16376 divisible by 4?
  23. 23.Is 5322 divisible by 3?
  24. 24.Is 7377 divisible by 2?
  25. 25.Is 16228 divisible by 13?
  26. 26.Is 91365 divisible by 15?
  27. 27.Is 11469 divisible by 4?
  28. 28.Is 19743 divisible by 7?
  29. 29.Is 16695 divisible by 7?
  30. 30.Is 25664 divisible by 8?
  31. 31.Is 62543 divisible by 13?
  32. 32.Is 188280 divisible by 30?
  33. 33.Is 198389 divisible by 29?
  34. 34.Is 103380 divisible by 20?
  35. 35.Is 42815 divisible by 11?
  36. 36.Is 60078 divisible by 17?
  37. 37.Is 15201 divisible by 3?
  38. 38.Is 1593 divisible by 12?
  39. 39.Is 64798 divisible by 11?
  40. 40.Is 16056 divisible by 24?

Answer key

  1. no
  2. no
  3. yes
  4. yes
  5. yes
  6. yes
  7. no
  8. no
  9. no
  10. no
  11. yes
  12. yes
  13. no
  14. yes
  15. yes
  16. yes
  17. yes
  18. no
  19. yes
  20. no
  21. yes
  22. yes
  23. yes
  24. no
  25. no
  26. yes
  27. no
  28. no
  29. yes
  30. yes
  31. yes
  32. yes
  33. yes
  34. yes
  35. no
  36. yes
  37. yes
  38. no
  39. no
  40. yes

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